THE OPTICS OF PTOLEMY 
295 
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. 96, ed. 
but the translation into Latin (uoav included in the Teubner 
edition of Heron, ii, 1900, pp. 316-64), which was made by 
William of Moerbeke in 1269, was evidently made from the 
Greek and not from the Arabic, as is shown by Graecisms in 
the translation. 
A mechanical work, lie pi po-n-wu. 
There are allusions in Simplicius 1 and elsewhere to a book 
by Ptolemy of mechanical content, vepl poncov, on balancings 
or turnings of the scale, in which Ptolemy maintained as 
against Aristotle that air or water (e.g.) in their own ‘ place ’ 
have no weight, and, when they are in their own ‘ place ’, either 
remain at rest or rotate simply, the tendency to go up or to 
fall down being due to the desire of things which are not in 
their own places to move to them. Ptolemy went so far as to 
maintain that a bottle full of air was not only not heavier 
than the same bottle empty (as Aristotle held), but actually 
lighter when inflated than when empty. The same work is 
apparently meant by the ‘ book on the elements ’ mentioned 
by Simplicius. 2 Suidas attributes to Ptolemy three Books of 
Mechanica. 
Simplicius 3 also mentions a single book, nepl diao-rao-emy, 
‘On dimension’, i.e, dimensions, in which Ptolemy tried to 
show that the possible number of dimensions is limited to 
three. 
* 
Attempt to prove the Parallel-Postulate. 
Nor should we omit to notice Ptolemy’s attempt to prove 
the Parallel-Postulate. Ptolemy devoted a tract to this 
subject, and Proclus 4 has given us the essentials of the argu 
ment used. Ptolemy gives, first, a proof of Eucl. I. 28, and 
then an attempted proof of I. 29, from which he deduces 
Postulate 5. 
I 
1 Simplicius on Arist. De caelo, p. 710. 14, Heib. (Ptolemy, ed. Heib., 
vol. ii, p. 268). 
2 lb., p. 20. 10 sq. 
3 lb., p. 9. 21 sq., (Ptolemy, ed. Heib., vol. ii, p. 265). 
4 Proclus on Eucl. I, pp. 362. 14 sq., 865. 7—867. 27 (Ptolemy, ed. Heib., 
vol. ii, pp. 266-70).